A fully automatic \(hp\)-adaptivity. (English) Zbl 0999.65121

Demkowicz, L.; Rachowicz, W.; Devloo, Ph.

J. Sci. Comput. 17, No. 1-4, 117-142 (2002).

Summary: We present an algorithm, and a 2D implementation for a fully automatic \(hp\)-adaptive strategy for elliptic problems. Given a mesh, the next, optimally refined mesh, is determined by maximizing the rate of decrease of the \(hp\)-interpolation error for a reference solution. Numerical results confirm optimal, exponential convergence rates predicted by the theory of \(hp\) methods.

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

hp finite elements; hp-adaptivity; elliptic problems; numerical results; convergence